Peri and Jack never meet due to Jack being a DreamWorks character, while Periwinkle is a Disney character.
Jack and Peri are both capable of flight and doing ice-related magic, that they use to bring winter to the world. As well as the fact that Jack has "Frost" as his last name, after he was reborn as a winter spirit, while Peri is a Frost-Talent fairy from the Winter Woods of Pixie Hollow. Which might be why they both have white colored hair and blue colored eyes, along with them wearing blue colored clothing. While the two come from different film series and company universes, they both have them knowing and getting close with other fairies, Toothiana's bird-like tooth fairies and other kinds of talent fairies from all around Pixie Hollow. Due to certain events both Jack and Peri were separated from their sisters, even though Peri and Tink were lucky to find and come up with a solution to bring warm and winter fairies together, Jack had lost his memories of his little sister after falling into the icy lake and was reborn as a winter spirit, based upon how he save her life. His memories of her and their times together returned to him after Jack opens his memory tooth box. Jack and Peri also have a white bearded friend that reside in cold places, the North Pole and the Winter Woods, where they are Santa Clause and the Keeper.
As a fairy from the magical world of Disney Fairies, Peri was born from a baby's first laugh. Jack on the other hand grows strength from the number of children who believe in him, after he became a guardian, but can only been seen by his believers before and after he became the Guardian of Fun, while Peri can be seen by humans without them believing in fairies. Unless that human were to say "I don't believe in fairies", since fairies from Neverland are known to die if they are near people who say those words. Just as the fading belief from the world's children causes a Guardian of Childhood to grow weak, while Jack hadn't had felt or went through that kind of fading away pain he did witness it happing to the North, Bunny, Sandy and Tooth. Periwinkle also hadn't been in or had witness a fairy dying from hearing those dangerous words, but does know a fairy nearly did die from those said words, Peri has been placed in the kind of danger precision that threatened her wings when she left the safety of the Winter Woods; and was lucky enough to return and recover in her winter home before she could loss her wings and her ability to fly for good. Just as Peri had nearly lost their ability to fly, Jack had briefly felt powerless when Pitch had snapped his staff in half, and was also luck enough to find the strength within him to repair it.
Both of their films originate from a children book series, Disney Fairies and Guardians of Childhood, while the two ice wielding characters were created and added in the CGI films. Sometimes after Rise of the Guardians came out the author of the Guardians of Childhood book series began to add Jack Frost to it, as the "incarnation" of the character that's Jack's design and the type of weapon he uses is drawn from, Nightlight.
Jack and Peri are two of the main members in the Secret of the Incredible Frozen Guardians crossover fandom, with Elsa from Frozen and Frozone from The Incredibles. Some have Jeriwinkle rival with Elswinkle and Jelsa, or ship all three ice wielding characters together in a polyship or a fanon familyship.
Because Peri is Tinker Bell's sister while Jack is seen as a Peter Pan-like character, from his ability to fly and is very close with on of Toothiana's fairies known as Baby Tooth, a few fans portray them as the letters in a Peter Pan AU. Some have even featured Jack as a fellow Frost-Talent fairy that is friends with Peri, or have Peri taking Baby Tooth's place in Jack's story. Along with a few fans sometimes having the two at the same height, commonly to around Jack's height and rarely have him around Peri's small fairy height. While the color scheme of their white hair and blue eye colors, has a few fans feature them as siblings, for fun. Since Peri is a magical being like Jack and the rest of the Guardians, she'll be able to see Jack without believing in him. Just as Jack's time with Tooth's fairies will have him being very fund and friendly with Peri.
While the ship isn't every popular on AO3, it doe has a reasonable size fanbase on DeviantArt, where there are two fan-made artwork clubs about it.